Evaluate learners' ability to analyze and compare error behavior and convergence rates of the Newton–Raphson and Secant methods for root-finding. Test understanding of theoretical orders of convergence (quadratic vs. superlinear ≈1.618), asymptotic error formulas and constants, sensitivity to initial guesses and derivative availability, typical failure modes, and interpretation of numerical experiment results (iteration counts and error-vs-iteration behavior) to assess practical trade-offs.